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Computational modeling

Posted by Arjendu on May 2, 2008

The ‘other’ class (that is, other than intro) that I’ve been teaching this term, is an interdisciplinary elective called ‘Computational modeling’; I am co-teaching it with my colleague Cindy Blaha, who is a galactic astronomer.

This is the second time I’ve taught this course. The first time was last year, with my fellow-theorist Bill Titus. This course grew out of funding from the last HHMI grant cycle, and is directed at students in geology or biology (preferably) to address the idea that (a) the typical biologist or geologist tends to be less comfortable/less prepared with mathematics than, say, the typical physicist and (b) there are a lot of cool problems in their fields amenable to quantitative analysis if only people in their fields would use some sort of modeling and that (c) current computational technology allows you to ‘code’ and model systems without being extremely mathematically or computationally adept necessarily.

I like teaching this course, and even more when I am not drowning in intro. I get to convey what I regard as the distillation of *my* scientific research attitude: Take a system you’d like to study, find a decent set of equations that capture the essence of the behavior, and then study the heck out of that system of equations. That is, ‘solve’ the equations using whatever tools you can deploy, and make predictions about the behavior of the system, and in the process generalize your study as much as possible — preferably capturing the dynamics in some broad intuitive explanations.

That I am ‘modeling’ nature in my studies was not entirely obvious to me until I spent some time collaborating with Randy Hulet as well as with Barry Dunning when I was at Rice. Let me explain what I mean by what might sound like a very silly comment: As a ‘typical’ theorist, I had gone through my thesis and my post-doc with an implicit attitude where I believed in the meaning and validity of the equations I was using as the absolute truth, and thought of an ‘experiment’ as a place where the equations were approximately realized. This shifted slowly during my time at Rice. The shift started when I finally visited Randy’s lab a few months after I started talking with him about a strange phenomenon in his Lithium 7 Bose-Einstein condensates (more on this elsewhere, if requested or if I get around to it). I spent an hour or so with his post-doc and grad students being walked through the ‘atom-trapping’ equipment — the optics and the magnets, and what not — the entire complicated process needed to cool the Lithium gas down to nano-kelvin temperatures before it condensed, and the way a signal was extracted from the system. The place was stuffed to the gills with tons of expensive equipment, all beautifully arranged and tuned to produce the effects needed. I walked out of there with a better understanding of what was going on in the experiment, but also feeling a little stunned that I had only one equation to describe all of this! (For the curious, this is the the Gross-Pitaevskii equation, a nonlinear Schrodinger equation, which is a mean-field description of the condensed atoms). Sure, this was a pretty mean and nasty equation, but it felt … inadequate.

And I would argue back and forth with Randy about what exactly he and his students were doing in their lab, and how we were trying to take care of that in the equations, steadily improving my hold on the exact correspondence between the theory and the experiment. Despite the tenuous connections, in general theorists AND experimentalists have a lot of trust in this equation, particularly because the predictions did so well. Something similar happened in my discussions with Barry Dunning’s group, though since he was working on a Rydberg atom in an almost classical state, as opposed to Randy’s condensate, the interpretation issues were a little less confusing.

These interactions with experimentalists were a wonderful education, and that’s when I got a better feel for the elaborate dance between theory and experiment — experimenters trying hard to reproduce the ‘idealized’ conditions of the theory, theorists trying to extract their best models for the experimental situation, and both negotiating on the interpretation of the correspondence.

And it is this sense that I am trying to convey to my students (all of whom are biologists or geologists, except for one physicist who is a pre-med, so he’s pretty up on the biology). The equations in physics are so much more reliable, the correspondence between reality and the math so much cleaner, than those describing the messy messy messy real world systems of biology and geology, so we really do have a head-start when we ‘model’ in physics. But surely some of that attitude can pay off elsewhere? That’s what’s the effort is with this class.


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